Scientific Series

Tensor product states are powerful tools for simulating area-law entangled states of many-body systems. The applicability of such methods to the non-equilibrium dynamics of many-body systems is less clear due to the presence of large amounts of entanglement. New methods seek to reduce the numerical cost by selectively discarding those parts of the many-body wavefunction, which are thought to have relatively litte effect on dynamical quantities of interest. We present a theory for the sizes of “backflow corrections”, i.e., systematic errors due to these truncation effects and introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. In the DAOE method, we represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We benchmark this scheme by calculating spin and energy diffusion constants in a variety of physical models and compare to other existing methods.

---

Zoom link 

In this talk the role of information theory in the description of physical evolutions will be discussed. After defining information quantifiers, their contractivity with respect to physical dynamics will be explained, a requirement which simply encodes the intuition that noisy transformations should lose information. The interplay between the two concepts will be exemplified for Markovian evolutions, showing how Markovianity can be defined in purely information theoretic terms. Extending on this result, we prove our main theorem: that all physical maps can be defined solely in terms of a particular metric on the space of density matrices, the Fisher information. This result should be understood in the context of reconstruction of quantum mechanics, proving once again the key role of information in shaping our description of the world.

---

Zoom link 

The two body problem in general relativity is of great theoretical and observational interest, and can be studied in the post-Newtonian, post-Minkowskian and small mass ratio approximations, as well as with effective one body and fully numerical techniques. An issue that arises is whether the motion can be decomposed into dissipative and conservative sectors for which the conservative sector admits a Hamiltonian description. This has been established to various orders in the post-Newtonian and post-Minkowskian approximations. In this talk, I will go over recent work where we showed that in the small mass ratio approximation, the motion of a (spinning) point particle under the conservative piece of the first-order self force is Hamiltonian in any stationary spacetime. After this, I describe two issues that arise when attempting to extend these results to subleading order in the mass ratio, namely infrared divergences and ambiguities in the conservative/dissipative splittings. I suggest resolutions of these issues and successfully derive a subleading Hamiltonian conservative sector for the scalar self force, as a toy model for the gravitational case.

---

Zoom link

The interplay of quantum fluctuations and interactions can yield novel quantum phases of matter with fascinating properties. Understanding the physics of such systems is a very challenging problem as it requires to solve quantum many body problems—which are generically exponentially hard to solve on classical computers. In this context, universal quantum computers are potentially an ideal setting for simulating the emergent quantum many-body physics. In this talk, I will discuss two different classes of quantum phases: First, we consider symmetry protected topological (SPT) phases and show that a topological phase transitions can be simulated using shallow circuits. We then utilize quantum convolutional neural networks (QCNNs) as classifiers and introduce an efficient framework to train them. Second, we focus on the realization of topological ordered phases and simulate the braiding of anyons. Taking into account additional symmetries, we then investigate phase transitions between different symmetry enriched topological (SET) phases.

---

Zoom link

Particle physics underpins our understanding of the world at a fundamental level by describing the interplay of matter and forces through gauge theories. Yet, despite their unmatched success, the intrinsic quantum mechanical nature of gauge theories makes important problem classes notoriously difficult to address with classical computational techniques. A promising way to overcome these roadblocks is offered by quantum computers, which are based on the same laws that make the classical computations so difficult. Here, we present a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. This computation is made possible by the use of a trapped-ion qudit quantum processor, where quantum information is encoded in different states per ion, rather than in two states as in qubits. Qudits are ideally suited for describing gauge fields, which are naturally high-dimensional, leading to a dramatic reduction in the quantum register size and circuit complexity. Using a variational quantum eigensolver, we find the ground state of the model and observe the interplay between virtual pair creation and quantized magnetic field effects. The qudit approach further allows us to seamlessly observe the effect of different gauge field truncations by controlling the qudit dimension. Our results open the door for hardware-efficient quantum simulations with qudits in near-term quantum devices.

--- 

Zoom link 

Topological strings are well understood in perturbation theory, but their non-perturbative structure has been the subject of much work and speculation. A useful approach to this problem is to unveil the non-perturbative sectors of the theory by looking at the large order behavior of the perturbative series. This approach can be formulated in a mathematically rigorous way by using the theory of resurgence. In this talk I review the basic ideas behind this approach and I show that it can be successfully applied to topological string theory on arbitrary Calabi-Yau threefolds. Thsee methods lead, not only to explicit non-perturbative topological string amplitudes, but also to a conjecture relating the “invariants” of the theory of resurgence (also known as Stokes constants) to BPS invariants. Physically, this conjecture implies that the large order behavior of the topological string perturbative series contains information about the spectrum of stable D-brane sectors.

---

Zoom link

Besides providing a possible explanation to the strong CP problem and dark matter, the QCD axion possesses a rich cosmology. For example, if PQ breaking occurs after inflation, then axion cosmic strings form. Near the QCD phase transition, every axion string become attached to a domain wall which pull on the strings and cause the string-wall network to decay. While every string becomes attached to a domain wall, it is possible, though rare, to form an enclosed domain wall that is not attached to any axion string. These enclosed domain walls collapse under their own self tension, compressing a large amount of energy into a small volume and thereby potentially forming a primordial black hole. In this talk, I will discuss the abundance of enclosed domain walls, their dynamics of collapse, the efficiency of black hole formation, and their relic abundance. For sufficiently large axion decay constants, there may be an observable gravitational lensing signal at future lensing telescopes, especially in models with axion-like-particles.

---

Zoom link

Both the social and natural world are replete with complex structure that often has a probabilistic interpretation. In the former, we may seek to model, for example, the distribution of natural images or language, for which there are copious amounts of real world data. In the latter, we are given the probabilistic rule describing a physical process, but no procedure for generating samples under it necessary to perform simulation. In this talk, I will discuss a generative modeling paradigm based on maps between probability distributions that is applicable to both of these circumstances. I will describe a means for learning these maps in the context of problems in statistical physics, how to impose symmetries on them to facilitate learning, and how to use the resultant generative models in a statistically unbiased fashion. I will then describe a paradigm that unifies flow-based and diffusion based generative models by recasting generative modeling as a problem of regression. I will demonstrate the efficacy of doing this in computer vision problems and end with some future challenges and applications.

---

Zoom link

I will review recent progress in the asymptotic safety approach to quantum gravity. This includes the computation of momentum-dependent graviton correlation functions, the structure of the Standard Model with asymptotically safe gravity, and the recent first computation directly in space-times with Lorentzian signatures via the spectral function of the graviton. Overall, I will display the progress towards the computation of the quantum effective action which encapsulates effective field theory in the IR limit and the asymptotic safety regime in the UV limit.

---

Zoom link

In the near future, where only a small number of companies and institutions will have access to large-scale quantum computers, it is essential that clients are able to delegate their computations in a secure way, without their data being accessible by the server. The field of blind quantum computation has emerged in recent years to address this issue, however, the majority of work on this topic has so far been restricted to the secure computation of sequences of quantum gates acting on a quantum state. Yet, a client capable of performing quantum subroutines may want to conceal not only their quantum states but also the subroutines they perform themselves. In this work, we introduce a framework of higher-order blind quantum computation, where a client performs a quantum subroutine (for example a unitary gate), which is transformed in a functional way by a server with more powerful quantum capabilities (described by a higher-order transformation), without the server learning about the details of the subroutine performed. As an example, we show how the DQC1 algorithm for estimating the trace of a unitary gate can be implemented securely by a server given only an (extended) black-box description of the unitary gate. Finally, we extend the framework to the case where the details of the server's algorithm are also concealed from the client.

---

Zoom link